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Multi-asset return risk measures

Published online by Cambridge University Press:  16 July 2025

Christian Laudagé Open the ORCID record for Christian Laudagé [Opens in a new window] ,
Felix-Benedikt Liebrich  and
Jörn Sass Open the ORCID record for Jörn Sass [Opens in a new window]
Christian Laudagé*
Affiliation:
Department of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Straße 47, 67663 Kaiserslautern, Germany
Felix-Benedikt Liebrich
Affiliation:
Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, Netherlands
Jörn Sass
Affiliation:
Department of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Straße 47, 67663 Kaiserslautern, Germany
*
Corresponding author: Christian Laudagé; Email: christian.laudage@rptu.de
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Abstract

We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk measures (MARRMs), introduces a novel economic model for multiplicative risk sharing. We point out the connection between MARRMs and the well-known concept of multi-asset risk measures (MARMs). Then, we conduct a case study, based on an insurance dataset, in which we use typical continuous-time financial markets and different notions of acceptability of losses to compare RRMs, MARMs, and MARRMs and draw conclusions about the cost of risk mitigation. Moreover, we analyze theoretical properties of MARRMs. In particular, we prove that a positively homogeneous MARRM is quasi-convex if and only if it is convex, and we provide conditions to avoid inconsistent risk evaluations. Finally, the representation of MARRMs via MARMs is used to obtain various dual representations.

Keywords

Multi-asset risk measurereturn risk measurerisk sharingdual representationsAverage-Return-at-RiskD81G10G32

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , First View , pp. 1 - 27
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The International Actuarial Association

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